A ground state hydrogen atom absorbs a photon of light having a wavelength of 92.05 nm. It then gives off a photon having a wavelength of 1736 nm. What is the final state of the hydrogen atom?

Absorbed photon energy

Ea = hc/λ ... (Planck's equation)

Ea = hc / 92.05^-9m

Energy emitted

Ee = hc / 1736^-9m

Energy retained ...

∆E = Ea - Ee = hc (1/92.05 ^-9 - 1/1736^-9)

∆E = (6.625^-34) (3.0^8) (1.028^7)

∆E = 2.04^-18 J

Converting J to eV (1.60^-19 J/eV)

∆E = 2.04^-18 / 1.60^-19

∆E = 12.70 eV

Ground state (n=1) energy for Hydrogen = - 13.60eV

New energy state = (-13.60 + 12.70) eV = - 0.85 eV

Energy states for Hydrogen

En = - (13.60 / n²)

n² = - 13.60 / - 0.85 = 16

n = 4